量子物理
[提交于 2025年4月2日
]
标题: 时间最优单标量控制在单位动力学的量子比特上
标题: Time-optimal single-scalar control on a qubit of unitary dynamics
摘要: Optimal control theory is applied to analyze the time-optimal solution with a single scalar control knob in a two-level quantum system without quantum decoherence. Emphasis is \change{placed} on the dependence on the maximum control strength $u_\text{max}$. General constraints on the optimal protocol are derived and used to rigorously parameterize the time-optimal solution. Two concrete problems are investigated. For generic state preparation problems, both multiple bang-bang and bang-singular-bang are legitimate and should be considered. Generally, the optimal is bang-bang for small $u_\text{max}$, and there exists a state-dependent critical amplitude above which singular control emerges. For the X-gate operation of a qubit, the optimal protocol \change{is exclusively} multiple bang-bang. The minimum gate time is about 80% of that based on the resonant Rabi $\pi$-pulse over a wide range of control strength; in the $u_\text{max} \rightarrow 0$ limit this ratio is derived to be $\pi/4$. To develop practically feasible protocols, we present methods to smooth the abrupt changes in the bang-bang control while preserving perfect gate fidelity. \change{The presence of bang-bang segments in the time-optimal protocol}表明高频分量和完整的计算(而不是通常采用的旋转波近似)对于最终的量子速度极限是必不可少的。
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